Determining Age of Windows Computer

Solution 1:

systeminfo | findstr /C:"Install Date"

and looking for the BIOS version will also give you a clue:

systeminfo | findstr /C:"BIOS Version"

Solution 2:

• If you have access to the physical internals of the computer, i.e. if you can open the case, and if you are willing to go through the trouble, you might find some date labels on some components (like the hard drive).
  I've used this method several times successfully, but it depends on where the computer was bought (small company, big vendor like Dell, internet, ...) and if they have a habit of sticking date labels to certain components.

• If it is a computer from a notable manufacturer (Dell, HP, Apple, ...) you might try to look for a sticker with a service tag, and enter that service tag somewhere on the company's website. Some vendors show the purchase date.